In the most general terms, a reason is a consideration which justifies or explains an action, a belief, an attitude, or a fact.
Normative reasons are what people appeal to when making arguments about what people should do or believe. For example, that a doctor's patient is grimacing is a reason to believe the patient is in pain. That the patient is in pain is a reason for the doctor to do things to alleviate the pain.
Explanatory reasons are explanations of why things happened. For example, the reason the patient is in pain is that her nerves are sending signals from her tissues to her brain.
A reason, in many cases, is brought up by the question "why?", and answered following the word because.